This novel was published in 2013 by Marie Lu.
The names of the protagonists match nearly perfectly: June Iparis and Daniel “Day” Altan Wing. According to Wikipedia, June is a soldier, as mentioned in the question:
June Iparis, a fifteen-year-old prodigy who scored a perfect 1500 on
her Trial, the Republic's mandatory test system. Born into an elite
Republic family, her parents were mysteriously killed in a car crash,
leaving Metias, her older brother, to care for her.
By contrast, Day is a criminal:
Daniel “Day” Altan Wing, a fifteen-year-old rebellious criminal born in the slums of the
Republic. Day is the Republic’s most-wanted criminal and the prime
suspect of Metias’s murder.
Indeed, he steals medicine and food, as mentioned in the question:
He once torched a whole squadron of fighter jets on an empty airfield
in the middle of the night and has on two occasions grounded airships
by crippling their engines. He once vandalized the side of a military
building. He’s stolen money, food, and goods. But he doesn’t set
roadside bombs. He doesn’t shoot soldiers. He doesn’t attempt
assassinations. He doesn’t kill.
There are indeed two other books in the series: Prodigy and Champion.
This may be the same book as here.